ah12049 said:
I have been thinking about the idea that the universe is infinite in size and have wondered if it is not also possible that the universe is infinite in time as well - that is to say, the universe has always been here and always will be here, that it doesn't have a beginning or an end. This idea is not consistent with the Big Bang which many people accept as true, but it seems to me that if the universe is infinite in size then it would take an infinite amount of time to decay, therefore it seems fair enough to say that the universe will always exist, so it seems only the next step to suggest that it has always existed. Is this idea possible?
If you are doing cosmology it is perfectly legitimate to assume that the universe has no end or beginning in time.
The standard model has no end---it continues expanding into the indefinite future.
Keep in mind that the standard cosmic model (so-called "LCDM" that pretty much every specialist in observational cosmology uses) might be WRONG. Scientists don't fully believe their models. They continue to challenge and test them to see if they need improvement. The currently accepted LCDM gives an amazingly good fit to the mountains of data that have accumulated from astronomical observation, but it is still
merely the best we have so far. Merely the most reliable accurate fit.
The fact that the standard model has a beginning--a point in time where it blows up and stops giving reasonable numbers--is widely considered to be a symptom that it is incomplete and needs fixing. It is apparently not applicable at extreme energy density, so it is not trusted. A considerable number of researchers have gotten interested in modifications of the standard cosmic model that include quantum effects on geometry at extreme density around start of expansion, and the modified models do not fail. No odd or "singular" behavior--no "blow-up" at the start of expansion. So in these models time just continues on back, not uncommonly into a
contracting phase. Quantum effects at high density cause the contraction to rebound.
It's certainly legitimate to assume that the universe goes back indefinitely in time, just as (according to standard LCDM) it goes forward indefinitely into the future. There are models that are time-infinite in both past and future, and which are just as good a fit to the data collected so far---recover the good fit of the LCDM.
But it is also legitimate to assume that it does NOT go back indefinitely. Cosmologists have a choice of models to work with (and presumably if they are wise they never fully commit to one or the other

)
I'm not talking about "multiverse" stuff. Ordinary cosmology just deals with the
universe we experience and with models we can hope to test by comparison with observation. There was a bubble of "multi" speculation in the mid 2000s---peaked sometime around 2003-2008. Since 2008 I've been seeing less and less mention at the professional level (i.e. conference talks and journal articles).